A017968 - OEIS

%I #28 Jul 29 2022 20:23:35

%S 1,5,21,96,441,2021,9261,42439,194481,891224,4084101,18715702,

%T 85766121,393029742,1801088541,8253624572,37822859361,173326116021,

%U 794280046581,3639848436450,16679880978201,76436817165460,350277500542221,1605173160474663,7355827511386641

%N Powers of sqrt(21) rounded to nearest integer.

%H Vincenzo Librandi, <a href="/A017968/b017968.txt">Table of n, a(n) for n = 0..1000</a>

%p a:= n-> round(sqrt(21)^n):

%p seq(a(n), n=0..25);  # _Alois P. Heinz_, Jul 29 2022

%t Floor[(Sqrt[21])^Range[0,25]+1/2] (* _Harvey P. Dale_, Sep 22 2011 *)

%o (PARI) a(n)=round(sqrt(21)^n) \\ _Charles R Greathouse IV_, Nov 18 2011

%o (Magma) [Round(Sqrt(21)^n): n in [0..30]]; // _Vincenzo Librandi_, Nov 20 2011

%o (Python)

%o from math import isqrt

%o def A017968(n): return (m:=isqrt(k:=21**n))+int((k-m*(m+1)<<2)>=1) # _Chai Wah Wu_, Jul 29 2022

%Y Cf. A010477 (sqrt(21)), A017967.

%Y Bisection gives A009965 (even part).

%K nonn

%O 0,2

%A _N. J. A. Sloane_